{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "6a264eba-42cc-4800-8369-24b0891d167d",
   "metadata": {
    "tags": []
   },
   "source": [
    "\n",
    "# Maximum Cut Problem\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f393b1d7-0ecd-4b99-9940-2ed55283c6b0",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "\n",
    "The \"Maximum Cut Problem\" (MaxCut) [[1](#MaxCutWiki)] is an example of combinatorial optimization problem. It refers to finding a partition of a graph into two sets, such that the number of edges between the two sets is maximal. This optimization problem is the cardinal example in the context of Quantum Approximate Optimization Algorithm [[2](#QAOA)], since it is an unconstrained problem whose objective function in terms quantum gates can be derived easily. With the Classiq platform, things are even simpler, as the objective function is inserted in its arithmetic form.\n",
    "\n",
    "## Mathematical formulation\n",
    "\n",
    "Given a graph $G=(V,E)$ with $|V|=n$ nodes and $E$ edges, a cut is defined as a partition of the graph into two complementary subsets of nodes. In the MaxCut problem we are looking for a cut where the number of edges between the two subsets is maximal. We can represent a cut of the graph by a binary vector $x$ of size $n$, where we assign 0 and 1 to nodes in the first and second subsets, respectively. The number of connecting edges for a given cut is simply given by summing over $x_i (1-x_j)+x_j (1-x_i)$ for every pair of connected nodes $(i,j)$.\n",
    "\n",
    "# Solving with the Classiq platform\n",
    "\n",
    "We go through the steps of solving the problem with the Classiq platform, using QAOA algorithm [[2](#QAOA)]. The solution is based on defining a pyomo model for the optimization problem we would like to solve."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "952d49b3-5dc6-41a1-8822-0622df536cf7",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:59:32.303785Z",
     "iopub.status.busy": "2024-05-07T15:59:32.303132Z",
     "iopub.status.idle": "2024-05-07T15:59:33.069587Z",
     "shell.execute_reply": "2024-05-07T15:59:33.068747Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "from typing import cast\n",
    "\n",
    "import networkx as nx\n",
    "import numpy as np\n",
    "import pyomo.core as pyo\n",
    "from IPython.display import Markdown, display\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60d446c0-15fb-4b1b-bc4f-f4ecd477168e",
   "metadata": {},
   "source": [
    "## Building the Pyomo model from a graph input\n",
    "\n",
    "We proceed by defining the pyomo model that will be used on the Classiq platform, using the mathematical formulation defined above:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "dc40bd2c-9a94-4a7c-bd3d-2533a6bd21d7",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:59:33.075318Z",
     "iopub.status.busy": "2024-05-07T15:59:33.073752Z",
     "iopub.status.idle": "2024-05-07T15:59:33.081384Z",
     "shell.execute_reply": "2024-05-07T15:59:33.080709Z"
    },
    "lines_to_next_cell": 2,
    "tags": []
   },
   "outputs": [],
   "source": [
    "# we define a function which returns 1 if two connected nodes are on a different subset, and 0 otherwise\n",
    "\n",
    "\n",
    "def arithmetic_eq(x1: int, x2: int) -> int:\n",
    "    return x1 * (1 - x2) + x2 * (1 - x1)\n",
    "\n",
    "\n",
    "# we define a function which returns the pyomo model for a graph input\n",
    "def maxcut(graph: nx.Graph) -> pyo.ConcreteModel:\n",
    "    model = pyo.ConcreteModel()\n",
    "    model.x = pyo.Var(graph.nodes, domain=pyo.Binary)\n",
    "\n",
    "    model.cost = pyo.Objective(\n",
    "        expr=sum(\n",
    "            arithmetic_eq(model.x[node1], model.x[node2])\n",
    "            for (node1, node2) in graph.edges\n",
    "        ),\n",
    "        sense=pyo.maximize,\n",
    "    )\n",
    "\n",
    "    return model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b5650177-cb88-4328-a581-ef2712e79dd8",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Generating a specific problem\n",
    "\n",
    "Let us pick a specific problem:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6212e51c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:59:33.086362Z",
     "iopub.status.busy": "2024-05-07T15:59:33.085220Z",
     "iopub.status.idle": "2024-05-07T15:59:33.406150Z",
     "shell.execute_reply": "2024-05-07T15:59:33.405395Z"
    },
    "pycharm": {
     "name": "#%%\n"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create graph\n",
    "G = nx.Graph()\n",
    "G.add_nodes_from([0, 1, 2, 3, 4])\n",
    "G.add_edges_from([(0, 1), (0, 2), (1, 2), (1, 3), (2, 4), (3, 4)])\n",
    "pos = nx.planar_layout(G)\n",
    "nx.draw_networkx(G, pos=pos, with_labels=True, alpha=0.8, node_size=500)\n",
    "maxcut_model = maxcut(G)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c546e02b-ed1b-4385-be65-5e20854bcc77",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Setting Up the Classiq Problem Instance\n",
    "\n",
    "In order to solve the Pyomo model defined above, we use the Classiq combinatorial optimization engine. For the quantum part of the QAOA algorithm (`QAOAConfig`) - define the number of repetitions (`num_layers`):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "4321c06c-235d-4313-a635-6b743a4e4858",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:59:33.411272Z",
     "iopub.status.busy": "2024-05-07T15:59:33.410042Z",
     "iopub.status.idle": "2024-05-07T15:59:35.808520Z",
     "shell.execute_reply": "2024-05-07T15:59:35.807852Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "from classiq import construct_combinatorial_optimization_model\n",
    "from classiq.applications.combinatorial_optimization import OptimizerConfig, QAOAConfig\n",
    "\n",
    "qaoa_config = QAOAConfig(num_layers=4)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a604f53f-355a-4591-b6b3-4fb1d05a4bf9",
   "metadata": {},
   "source": [
    "For the classical optimization part of the QAOA algorithm we define the maximum number of classical iterations (`max_iteration`) and the $\\alpha$-parameter (`alpha_cvar`) for running CVaR-QAOA, an improved variation of the QAOA algorithm [[3](#cvar)]:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "0df30f52-9c65-4ecb-bfc1-62a3b2c96cd7",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:59:35.811745Z",
     "iopub.status.busy": "2024-05-07T15:59:35.811054Z",
     "iopub.status.idle": "2024-05-07T15:59:35.814525Z",
     "shell.execute_reply": "2024-05-07T15:59:35.813949Z"
    },
    "pycharm": {
     "name": "#%%\n"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "optimizer_config = OptimizerConfig(max_iteration=60, alpha_cvar=0.7)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "028d688e-9089-414b-9f7b-8421068642cc",
   "metadata": {},
   "source": [
    "Lastly, we load the model, based on the problem and algorithm parameters, which we can use to solve the problem:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "01bc439b-94cb-4bb6-90ce-4f29639779d0",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:59:35.816910Z",
     "iopub.status.busy": "2024-05-07T15:59:35.816601Z",
     "iopub.status.idle": "2024-05-07T15:59:35.888438Z",
     "shell.execute_reply": "2024-05-07T15:59:35.887774Z"
    },
    "pycharm": {
     "name": "#%%\n"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "qmod = construct_combinatorial_optimization_model(\n",
    "    pyo_model=maxcut_model,\n",
    "    qaoa_config=qaoa_config,\n",
    "    optimizer_config=optimizer_config,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "de903871-3483-4ad4-90d3-e5ca1b9d6722",
   "metadata": {},
   "source": [
    "We also set the quantum backend we want to execute on:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "345fa189-05af-49e7-abbe-3d3a4890aa8c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:59:35.891443Z",
     "iopub.status.busy": "2024-05-07T15:59:35.890972Z",
     "iopub.status.idle": "2024-05-07T15:59:35.898583Z",
     "shell.execute_reply": "2024-05-07T15:59:35.897990Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "from classiq import set_execution_preferences\n",
    "from classiq.execution import ClassiqBackendPreferences, ExecutionPreferences\n",
    "\n",
    "backend_preferences = ExecutionPreferences(\n",
    "    backend_preferences=ClassiqBackendPreferences(backend_name=\"aer_simulator\")\n",
    ")\n",
    "\n",
    "qmod = set_execution_preferences(qmod, backend_preferences)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "5a8d9402-7edb-4ae9-9536-95561df455e7",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:59:35.901011Z",
     "iopub.status.busy": "2024-05-07T15:59:35.900620Z",
     "iopub.status.idle": "2024-05-07T15:59:35.908526Z",
     "shell.execute_reply": "2024-05-07T15:59:35.907954Z"
    }
   },
   "outputs": [],
   "source": [
    "from classiq import write_qmod\n",
    "\n",
    "write_qmod(qmod, \"max_cut\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0398f8d3-d9d4-4f03-92b4-d34e20766767",
   "metadata": {},
   "source": [
    "## Synthesizing the QAOA Circuit and Solving the Problem\n",
    "\n",
    "We can now synthesize and view the QAOA circuit (ansatz) used to solve the optimization problem:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "3cab4848-bd66-4099-94b1-84c88e7a586c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:59:35.910977Z",
     "iopub.status.busy": "2024-05-07T15:59:35.910620Z",
     "iopub.status.idle": "2024-05-07T15:59:38.357365Z",
     "shell.execute_reply": "2024-05-07T15:59:38.356617Z"
    },
    "pycharm": {
     "name": "#%%\n"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Opening: https://platform.classiq.io/circuit/7217a54b-03a1-446e-9c66-b87ca4266918?version=0.41.0.dev39%2B79c8fd0855\n"
     ]
    }
   ],
   "source": [
    "from classiq import show, synthesize\n",
    "\n",
    "qprog = synthesize(qmod)\n",
    "show(qprog)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c7fdcaff-2d30-4f4f-a338-6b73ef8dc284",
   "metadata": {},
   "source": [
    "We now solve the problem by calling the `execute` function on the quantum program we have generated:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "5d2ab2da-f452-45db-9abe-f5b919ccdad3",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:59:38.361697Z",
     "iopub.status.busy": "2024-05-07T15:59:38.360464Z",
     "iopub.status.idle": "2024-05-07T15:59:41.841533Z",
     "shell.execute_reply": "2024-05-07T15:59:41.840741Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "from classiq import execute\n",
    "\n",
    "res = execute(qprog).result()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5dd7082a-7f61-47c4-a1c2-ef972583ab9b",
   "metadata": {},
   "source": [
    "We can check the convergence of the run:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "aa6542a6-3334-46ad-803a-ce4368686a63",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:59:41.845373Z",
     "iopub.status.busy": "2024-05-07T15:59:41.845072Z",
     "iopub.status.idle": "2024-05-07T15:59:41.877856Z",
     "shell.execute_reply": "2024-05-07T15:59:41.877102Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<PIL.JpegImagePlugin.JpegImageFile image mode=RGB size=640x480>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from classiq.execution import VQESolverResult\n",
    "\n",
    "vqe_result = res[0].value\n",
    "vqe_result.convergence_graph"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "38caaf41-152e-4c20-a0b8-418df875fc61",
   "metadata": {
    "tags": []
   },
   "source": [
    "# Optimization Results"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "50561ce0-f50f-4408-bd13-be795f077da1",
   "metadata": {},
   "source": [
    "We can also examine the statistics of the algorithm:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "81f03001-116c-4a5e-bbaf-b99390a93a6f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:59:41.881417Z",
     "iopub.status.busy": "2024-05-07T15:59:41.881167Z",
     "iopub.status.idle": "2024-05-07T15:59:41.923720Z",
     "shell.execute_reply": "2024-05-07T15:59:41.922966Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>probability</th>\n",
       "      <th>cost</th>\n",
       "      <th>solution</th>\n",
       "      <th>count</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.201</td>\n",
       "      <td>5.0</td>\n",
       "      <td>[0, 0, 1, 1, 0]</td>\n",
       "      <td>201</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.187</td>\n",
       "      <td>5.0</td>\n",
       "      <td>[1, 1, 0, 0, 1]</td>\n",
       "      <td>187</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.171</td>\n",
       "      <td>5.0</td>\n",
       "      <td>[0, 1, 0, 0, 1]</td>\n",
       "      <td>171</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.199</td>\n",
       "      <td>5.0</td>\n",
       "      <td>[1, 0, 1, 1, 0]</td>\n",
       "      <td>199</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.040</td>\n",
       "      <td>4.0</td>\n",
       "      <td>[1, 0, 0, 1, 1]</td>\n",
       "      <td>40</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   probability  cost         solution  count\n",
       "0        0.201   5.0  [0, 0, 1, 1, 0]    201\n",
       "2        0.187   5.0  [1, 1, 0, 0, 1]    187\n",
       "3        0.171   5.0  [0, 1, 0, 0, 1]    171\n",
       "1        0.199   5.0  [1, 0, 1, 1, 0]    199\n",
       "4        0.040   4.0  [1, 0, 0, 1, 1]     40"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "from classiq.applications.combinatorial_optimization import (\n",
    "    get_optimization_solution_from_pyo,\n",
    ")\n",
    "\n",
    "solution = get_optimization_solution_from_pyo(\n",
    "    maxcut_model, vqe_result=vqe_result, penalty_energy=qaoa_config.penalty_energy\n",
    ")\n",
    "optimization_result = pd.DataFrame.from_records(solution)\n",
    "optimization_result.sort_values(by=\"cost\", ascending=False).head(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9c0f654-5a4e-439b-b4a7-b363ed8f7d4b",
   "metadata": {},
   "source": [
    "And the histogram:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "5c0cfa66-7e4d-49c8-8aa7-772f3b8ec59f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:59:41.928752Z",
     "iopub.status.busy": "2024-05-07T15:59:41.927402Z",
     "iopub.status.idle": "2024-05-07T15:59:42.297140Z",
     "shell.execute_reply": "2024-05-07T15:59:42.296416Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[<Axes: title={'center': 'cost'}>]], dtype=object)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "optimization_result.hist(\"cost\", weights=optimization_result[\"probability\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "849aec45-d701-4ff8-bae3-005ef8e3df6e",
   "metadata": {},
   "source": [
    "Let us plot the solution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "6f946baa-8922-4901-ab1d-430d68712975",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:59:42.299963Z",
     "iopub.status.busy": "2024-05-07T15:59:42.299501Z",
     "iopub.status.idle": "2024-05-07T15:59:42.453905Z",
     "shell.execute_reply": "2024-05-07T15:59:42.453204Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "best_solution = optimization_result.solution[optimization_result.cost.idxmax()]\n",
    "\n",
    "colors = [\"r\" if best_solution[i] == 0 else \"g\" for i in range(5)]\n",
    "nx.draw_networkx(\n",
    "    G, pos=pos, with_labels=True, alpha=0.8, node_size=500, node_color=colors\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "831bcd2b-0def-4c6c-a52d-c06aba0cc3e2",
   "metadata": {},
   "source": [
    "## Classical optimizer results"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "762a3309-d73c-405b-a4a1-7442ab752245",
   "metadata": {},
   "source": [
    "Lastly, we can compare to the classical solution of the problem:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "19694867-7c19-4f15-90cd-2b8ea2179e46",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:59:42.456870Z",
     "iopub.status.busy": "2024-05-07T15:59:42.456216Z",
     "iopub.status.idle": "2024-05-07T15:59:42.553895Z",
     "shell.execute_reply": "2024-05-07T15:59:42.553267Z"
    },
    "pycharm": {
     "name": "#%%\n"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model unknown\n",
      "\n",
      "  Variables:\n",
      "    x : Size=5, Index=x_index\n",
      "        Key : Lower : Value : Upper : Fixed : Stale : Domain\n",
      "          0 :     0 :   0.0 :     1 : False : False : Binary\n",
      "          1 :     0 :   0.0 :     1 : False : False : Binary\n",
      "          2 :     0 :   1.0 :     1 : False : False : Binary\n",
      "          3 :     0 :   1.0 :     1 : False : False : Binary\n",
      "          4 :     0 :   0.0 :     1 : False : False : Binary\n",
      "\n",
      "  Objectives:\n",
      "    cost : Size=1, Index=None, Active=True\n",
      "        Key  : Active : Value\n",
      "        None :   True :   5.0\n",
      "\n",
      "  Constraints:\n",
      "    None\n"
     ]
    }
   ],
   "source": [
    "from pyomo.opt import SolverFactory\n",
    "\n",
    "solver = SolverFactory(\"couenne\")\n",
    "solver.solve(maxcut_model)\n",
    "\n",
    "maxcut_model.display()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "524d8a2f-a7a3-4a9d-8533-5b2f556455f9",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:59:42.557332Z",
     "iopub.status.busy": "2024-05-07T15:59:42.557008Z",
     "iopub.status.idle": "2024-05-07T15:59:42.708494Z",
     "shell.execute_reply": "2024-05-07T15:59:42.707802Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "solution = [pyo.value(maxcut_model.x[i]) for i in G.nodes]\n",
    "colors = [\"r\" if best_solution[i] == 0 else \"g\" for i in range(5)]\n",
    "nx.draw_networkx(\n",
    "    G, pos=pos, with_labels=True, alpha=0.8, node_size=500, node_color=colors\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "32714940-bc95-4cdb-98d1-904dcc80d00d",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    },
    "tags": []
   },
   "source": [
    "\n",
    "## References\n",
    "\n",
    "<a id='MaxCutWiki'>[1]</a>: [Maximum Cut Problem (Wikipedia)](https://en.wikipedia.org/wiki/Maximum_cut)\n",
    "\n",
    "<a id='QAOA'>[2]</a>: [Farhi, Edward, Jeffrey Goldstone, and Sam Gutmann. \"A quantum approximate optimization algorithm.\" arXiv preprint arXiv:1411.4028 (2014).](https://arxiv.org/abs/1411.4028)\n",
    "\n",
    "<a id='cvar'>[3]</a>: [Barkoutsos, Panagiotis Kl, et al. \"Improving variational quantum optimization using CVaR.\" Quantum 4 (2020): 256.](https://arxiv.org/abs/1907.04769)\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
